In the second screen shot, the date is a continuous field (notice the green pill), which is why it is giving the date an axis. To get the desired outcome, right click on the date again and select the first instance on More>Custom... Then, choose Month/Day/Year from the drop down menu.
Another option is for when you place this field on the view, drag it out holding down the right click button. Then, choose the appropriate date type.
Hope this helps!
Can you tell me what you mean by the 'green pill'? Do you mean that in the Rows, the box is green rather than blue?